A
acceptable quality level, 170
acceptance number, 168
acceptance region, 332
acceptance sampling, 167, 274
alternative hypothesis, 332
analysis of variance, 428
one-way, 428
two-way, 433
AOL, 170
asymptotically unbiased estimator, 281
asymptotically efficient estimator, 286
axiomatic approach (to probability), 22
B
bar chart, 67-68
Bayes criterion, 270, 272
Bayes risk, 270
Bayes theorem, 46
Bayesian estimation, 303
Bernoulli distribution, 145
beta distribution, 182
beta function, 182
bias, 255
sampling, 308
binomial coefficient, 11-12
binomial distribution, 146
mean and variance, 148
moment generating function, 151
bivariate normal distribution, 194
bivariate normal surface, 197
block
effects, 431
sum of squares, 432
boundary, class, 103
C
Cauchy distribution, 183
cell frequencies (contingency tables), 368
Chebyshev's theorem, 124
central limit theorem, 234
chi-square distribution, 180, 240, 324, 363
choices, multiplication of, 2
circular normal distribution, 197
circular permutations, 6
class, 103
boundary, 103
frequencies, 103
interval, 103
limits, 103
mark, 104, 419
coefficient, binomial, 11-12
combinations, 8
complement (of an event), 26
completely randomized design, 431
composite hypothesis, 331
compound events, 2
computer simulation, 150
conditional density, 96
conditional distribution, 95, 98, 100
joint, 98
conditional mean, 138
conditional variance, 138
conditional probability, 37-38
confidence interval, 312
difference of two proportions, 323
one-sided, 315
proportion, 321
regression coefficient, 396
confounding, 413, 424
consistency criterion, 56
consistent estimator, 289
consumer's risk, 170
contingency coefficient, 375
contingency table, 371
continuity correction, 192
continuous random variable, 73
controlled experiment, 430
convergence in probability, 289
correction term, 428
correlation coefficient, 195, 387
sample, 399
correlation analysis, 393
count data, 365
counting, 2
covariance, 126, 131
cumulant, 193
Cramer-Rao inequality, 283
critical region, 333
most powerful, 336
critical values, 354
cumulative distribution, 68, 77, 110
D
decision function, 268
degrees of freedom, 180, 244
De Morgan laws, 27
density function
conditional, 96
probability, 75
joint probability, 85
discrete random variable, 64
discrete uniform distribution, 144
distribution
Bernoulli, 145
beta, 182
binomial, 146
Cauchy, 183
chi-square, 180, 240
conditional, 95, 98, 100
cumulative, 68
F, 247, 326
frequency, 102
function, 68, 77
geometric, 154
gamma, 178
hypergeometric, 155
joint marginal, 94, 101
log-normal, 230
mean, 121
marginal, 92, 100
multinomial, 165
multivariate, 82
negative binomial, 153
normal, 185
Pareto, 184
Poisson, 159
posterior, 303
prior, 303
probability, 64
Rayleigh, 184
sampling, 233
Student t, 244, 315
uniform, 144, 176
univariate, 82
variance, 122
Weibull, 184
distribution-free tests, 453
double stem display, 102
Duncan multiple-range test, 441
E
effects, 425
interaction, 436
main, 436
treatment, 425
element (of sample space), 22
elimination, rule of, 46
estimator, 279
asymptotically efficient, 286
asymptotically unbiased, 281
consistent, 289
efficient, 284
interval, 279, 312
maximum likelihood, 298
minimum variance unbiased, 283
point, 279
sufficient, 291
unbiased, 280
events, 2, 25
complement, 26
equally likely, 31
independent, 42
intersection, 26
mutually exclusive, 27
pairwise independent, 44
union, 26
equalizer principle, 271
equally-likely events, 31
equitable game, 263
error mean square, 427
expectation, mathematical, 112
conditional, 137
expected cell frequencies, 368
expected value, 112
product of independent variables, 134
experiment, 22
controlled, 430
factorial, 435
one-way, 428
two-way, 433
fractional replicate of, 447
experimental design, 424
Latin square, 443
incomplete block, 444
exploratory data analysis, 356
exponential distribution, 179
two-parameter, 302
extrapolation, 418
F
F distribution, 247, 326
factorial experiments, 435
2^n factorials, 447
factorial moments, 152
factorial moment generating function, 151
factorization theorem, 293
factors, 435
failure rate, 164
finite population correction factor, 239
finite sample space, 23
fractional replicate, 447
frequency, class, 103
frequency distribution, 102
cumulative, 110
frequency polygon, 110
frequency interpretation (probability), 21, 50
G
games, theory of, 260
gamma distribution, 178
general addition rule, 33
geometric distribution, 154
H
H test, 464
histogram, 66
skewed, 105
hypergeometric distribution, 155
multivariate, 167
hypothesis
alternative, 332
composite, 331
simple, 331
test statistic for, 332
tests of, 331
inclusion-exclusion principle, 33
incomplete block designs, 444
independence, 42
of discrete random variables, 98
and covariance, 137
pairwise, 44
and variance, 136
interaction, 435
intersection (of events), 26
interval, class, 103
interval estimator, 279
invariance property, 301
J
Jacobian, 218
joint conditional distribution, 98
joint marginal distribution, 94, 101
joint moment-generating function, 139
joint probability distribution, 83
joint probability density, 85
K
Kruskal-Wallis test, 464
kurtosis, 129
L
large-sample test
law of large numbers, 234
Latin square design, 443
leaf, 102
least significant range, 442
least squares, 388
estimate, 389
level of significance, 333, 343, 352
likelihood function, 298
likelihood ratio test, 343
likelihood ratio statistic, 344
limits of prediction, 398
log-normal distribution, 230
loss function, 261
lot tolerance percentage defective, 170
M
main effects, 436
Mann-Whitney test, 460
marginal distribution, 92, 100-101
Markov's inequality, 130
mathematical expectation, 112
maximum likelihood, 297
estimator, 298
method of, 297
mean, 121
of binomial distribution, 148
conditional, 138
of Poisson distribution, 162
sample, 140
sampling distribution of, 233
standard error of, 233
mean-square error, 286
mean square
treatments, 428
median, 141, 252
method of least squares, 388
method of moments, 296
minimax criterion, 270
minimax strategy, 263
minimum variance unbiased estimator, 283
mode, 106
moments, 120
about the mean, 121
about the origin, 121
factorial, 152
of linear combinations, 135
method of, 296
moment generating function, 126
of binomial distribution, 151
of normal distribution, 186
of Poisson distribution, 162
factorial, 152
joint, 139
multinomial distribution, 167
multiple comparisons, 435
multiple-range test, 441
multiple regression, 392, 406
coefficients, 403, 407
residuals, 414
multiplication of choices, 2, 4
multiplication rule (of probabilities), 40
multivariate distribution, 82
hypergeometric, 165
mutually exclusive events, 27
N
negative binomial distribution, 153
Neyman-Pearson lemma, 336
nonparametric statistics, 251, 453
normal distribution, 185
bivariate, 194
circular, 197
moment-generating function, 186
standard, 187
normal equations, 390
normal regression analysis, 393
normal score, 198
O
observed cell frequencies, 368
OC curve, 168
odds, 36
ogive, 110
one-sided confidence interval, 315
one-way analysis of variance, 428
operating characteristic curve, 168, 341
order statistics, 251
outcome (of experiment), 22
outlier, 200
P
P-value, 355
pairwise independent
events, 44
random variables, 99
parallel system, 50
reliability of, 51
parameter space, 343
Pareto distribution, 184
partition, 9
Pascal distribution, 153
Pascal's triangle, 13
payoff matrix, 262
p.d.f., 76
permutations, 4, 5
circular, 6
Petersburg paradox, 120
pivotal method, 316
point estimator, 279
Poisson distribution, 159
mean and variance, 162
moment-generating function, 162
Poisson process, 180
pooled estimator, 318
population, 231
median, 253
posterior distribution, 303
power function of a test, 340
prediction, limits of, 398
prior distribution, 303
probability, 28
of acceptance, 168
conditional, 37-38
consistency criterion, 56
convergence in, 289
density function, 75
distribution, 65
equally-likely events, 31
general addition rule, 33
histogram, 66
multiplication rule, 40
rule of elimination, 46
special addition rule, 33
subjective method, 50
probability density, 74
joint, 85
probability distribution, 64
joint, 83
probability integral transformation, 215
producer's risk, 170
product moments, 130
about the mean, 131
about the origin, 130
proportions
confidence interval for, 324
difference (confidence interval), 323
pure strategy, 265
tests concerning, 365
R
random error, 255
random variable, 61-62
continuous, 73
discrete, 64
expected value, 112
random sample, 232
finite population, 237
randomized response technique, 59
randomized strategy, 265
randomizing, 424
range, 142
least significant, 442
rank-correlation coefficient, 470
rank-sum tests, 460, 464
sample, 142, 254
Rayleigh distribution, 184
replication, 425
regression, 382
bivariate, 382
coefficients, 386
confidence interval for beta, 396
normal regression analysis, 393
regret, 277
rejection region, 333
reliability, 50
of parallel system, 51
of series system, 50
repeated trials, 145
risk function, 268
robustness, 295, 452
runs, test based on, 466
S
saddle point, 264
sample space, 22
countable, 23
discrete, 23
finite, 23
sample
correlation coefficient, 399
mean, 140, 232, 237
median, 252
random, 232
range, 142, 254
sampling bias, 308
size, 233
standard deviation, 141
variance, 237
sampling
distribution, 233
distribution of the mean, 233
inspection, 167
plan, 168
without replacement, 40
sign test, 453
one-sample, 455
paired-sample, 455
signed-rank test, 456
significance tests, 343, 352
strategies, 261
series system, reliability of, 50
significance, level of, 333
simple hypothesis, 331
simulation, 150
skewness, 105, 129
Spearman's rank-correlation coefficient, 470
special addition rule, 33
standard deviation, sample, 141
standard error of the mean, 233
standard form (standardizing), 129
standard normal distribution, 187
statistic, 231
statistical games, 267
stem, 102
subjective method (probability), 50
sufficient estimator, 291
sum of squares, 427
T
T distribution, 244, 315, 358, 360, 395
test of hypothesis, 331
acceptance region for, 332
goodness of fit, 373
large-sample, 357
likelihood ratio test, 343
operating characteristic curve, 341
power, 336
power function, 340
rejection region for, 332
sequential, 343
type I error, 333
type II error, 333
uniformly most powerful, 342
tests of significance, 343, 352
theory of games, 260
tolerance limits, 254
treatment effects, 425, 431
Latin square design, 444
treatment mean square, 428
treatments, 426
tree diagram, 3
trials, repeated, 145
triangular probability density, 220
two-sample t test, 360
two way analysis of variance, 433
type I and type II errors, 333
U
U test, 460
unbiased estimator, 280
uniform distribution, 144, 176
union (of events), 26
univariate distribution, 82
V
variance, 122
of binomial distribution, 148
conditional, 138
of linear combination, 136
variance-ratio distribution, 249
Venn diagram, 26-27
W
waiting time, 179
Weibull distribution, 184
Wilcoxon signed-rank test, 456
Wilcoxon test, 460
Z
zero-sum two-person game, 261